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To deal with the strong attenuation of neutral particle flux in matter, like in radiation shielding studies, several techniques are used in Monte Carlo transport codes (MCNP, MCBEND, TRIPOLI, etc.) to accelerate the simulation of neutron or gamma ray transport. The exponential transform is one of the techniques that has been applied by using first- and/or second-degree analytical importance functions. The present work extends the application of this technique to an analytical toroidal form of the importance function. In this case, the sampling of the particle track length involves the solution of a fourth-degree equation. The practical usefulness of this work can be found for neutron and gamma ray transport studies related to thermonuclear fusion tokamak devices, for example.